Are there infinitely many unitary transformations to satisfy the relation $U\left| b \right\rangle = \left| a \right\rangle $ (where $UU^{\dagger} = U^{\dagger}U=1$) between two arbitrary, normalized real vectors? For having infinitely many unitary transformations, I think the two vectors must have same norms and this is a crucial condition. Am I right?
2026-03-27 00:02:02.1774569722
Do exist infinitely many unitary transformations between two real vectors?
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